A269554 Expansion of (3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1).

-1, -343, -33861, -3318283, -325158121, -31862177823, -3122168268781, -305940628162963, -29979059391701841, -2937641879758617703, -287858925156952833301, -28207237023501619046043, -2764021369378001713679161, -270845886962020666321511983, -26540132900908647297794495421

Offset

0,2

Comments

Mc Laughlin (2010) gives an identity relating ten sequences, denoted a_k, b_k, ..., f_k, p_k, q_k, r_k, s_k. This is the sequence q_k.

Links

Table of n, a(n) for n=0..14.

J. Mc Laughlin, An identity motivated by an amazing identity of Ramanujan, Fib. Q., 48 (No. 1, 2010), 34-38.

Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

Formula

G.f.: (3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1).

a(n) = 31/12 + ((17*sqrt(6) - 43)/(2*sqrt(6) + 5)^(2*n) - (17*sqrt(6) + 43)*(2 sqrt(6) + 5)^(2*n))/24. - Bruno Berselli, Mar 02 2016

Mathematica

CoefficientList[Series[(3 x^2 + 244 x + 1)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[Simplify[31/12 + ((17 Sqrt[6] - 43)/(2 Sqrt[6] + 5)^(2 n) - (17 Sqrt[6] + 43) (2 Sqrt[6] + 5)^(2 n))/24], {n, 0, 20}] (* Bruno Berselli, Mar 02 2016 *)

Prog

(PARI) Vec((3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))
(Sage)
gf = (3*x^2+244*x+1)/(x^3-99*x^2+99*x-1)
print(taylor(gf, x, 0, 20).list()) # Bruno Berselli, Mar 02 2016
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((3*x^2+244*x+1)/(x^3-99*x^2+99*x-1))); // Bruno Berselli, Mar 02 2016

Crossrefs

Cf. A261004, A269548, A269549, A269550, A269551, A269552, A269553, A269555, A269556.

Sequence in context: A270820 A140250 A117197 * A046236 A294663 A222460

Adjacent sequences: A269551 A269552 A269553 * A269555 A269556 A269557

Keyword

sign,easy

Author

Michel Marcus, Feb 29 2016

Status

approved